1. Field of the Invention
The present invention relates to methods for imaging gamma rays, and more specifically, it relates to the use of filtered back-projection algorithms for gamma radiation imaging with Compton cameras.
2. Description of Related Art
Compton cameras were first proposed as a method of imaging gamma radiation in Todd et al., Nature 251, 132-134 (1974). During the 1970s and 1980, Manbir Singh and his group at USC attempted to build and produce images with a Compton camera. Their attempts were not very successful due to technical problems associated with the detectors and image reconstruction problems associated with the Compton “scatter cone.” The events detected in a Compton camera define a scatter cone, but not the direction of the incident gamma ray. A mathematical reconstruction algorithm is required to convert information provided by the Compton camera into a source distribution. In Computed Tomography (CT), Single Photon Emission Tomography (SPECT), Positron Emission Tomogrpahy (PET) and Magnetic Resonance Imaging (MRI), the images are (generally) reconstructed using a class of (non-iterative) algorithms called filtered back-projection algorithms. However, Singh and his group were unable to find a filtered back-projection algorithm appropriate for Compton cameras. Instead, they began using iterative algorithms associated with maximum likelihood. These algorithms have the advantage that one need not perform detailed mathematical analysis of the imaging system, but are generally slow (due to iteration) and produce variable results (depending on stopping conditions and the numerical methods used). As a result of Singh's work, most researchers abandoned the search for a filtered back-projection algorithm for Compton cameras; maximum likelihood reconstructions were adopted as the standard in Compton camera research.
In the 1990s, a group headed by Les Rogers at the University of Michigan built a much more sophisticated Compton camera for medical imaging. Once again, iterative maximal-likelihood algorithms were used for the reconstruction. Furthermore, Rogers was assisted by a large group of experts in maximal-likelihood reconstruction at the University of Michigan headed by Jeff Fessler. Despite improved detector technology and the assembled expertise in iterative reconstruction, the images remained disappointing. Not only was the detector sensitivity too low for clinical applications, the (iterative) reconstruction required days of execution time on supercomputers. After this result, Compton cameras seemed to be a failed technology.
In the mid 1990s, however, a combination of new detector technology and more-sophisticated mathematics revived hopes for the Compton camera. The new technology involved solid-state detectors with improved energy and spatial resolution. (Energy resolution is crucial in Compton cameras because the “scatter cones” are determined by the energy deposition in the detectors.) More relevant, researchers began reexamining the Compton reconstruction algorithm. The filtered back-projection algorithms that had been abandoned by Singh and Rogers were revived by new mathematical insights. In 1994 Cree and Bonos published a paper (IEEE Trans on Medical imagining MI-13, 398-407 (1994)) that suggested that analytic inversion of the Compton reconstruction problem was possible. Shortly thereafter, Basko, Zeng, and Gullberg (Physics in Medicine and Biology 43, 887-894 (1996)) published a mathematical algorithm for Compton camera reconstruction that involved complicated sums of spherical harmonics. The major contribution of Basko et al. was the development of a rapid method for the evaluation of these summations. Basko et al. received U.S. Pat. No. 5,861,627 on this reconstruction technique in 1999. In 2000, Lucas Parra published a more mathematically rigorous inversion of the Compton camera reconstruction problem (IEEE Trans on Nuclear Science NS47, 1543-1550 (2000)). Once again, spherical harmonics were crucial in the analysis and, despite the greater rigor, Parra's technique relied on an infinite summation of spherical harmonics that was numerically slow and produced truncation errors when halted with only a finite number of terms. In 2002, T Tomitani and M. Hirasawa published a slightly different reconstruction algorithm (Physics in Medicine and Biology, 47, 2129-2145 (2002)) based, once again, on spherical harmonics. Unlike Parra, Tomitani and Hirasawa examined the truncation errors associated with termination of the infinite sum of spherical harmonics and demonstrated that the errors could be made small. In a second publication, Tomitani and Hirasawa (Physics in Medicine and Biology, 48, 1009-1029 (2003)) compensated for energy resolution errors and Doppler broadening—once again using spherical harmonic summations.
Since the 1970s, when the problem of Compton reconstruction was first studied, most researchers have decomposed the reconstruction into two parts. In the first part of the problem, the Compton camera is held in a fixed position with a source distribution (of gamma rays) located far away. In this part of the problem, one wants to determine the flux of incident radiation impinging on the camera from different directions. Because the Compton camera only provides information about the Compton scatter cone, one cannot assign a specific incident direction to individual events. However, if one accumulates enough events for a statistical analysis, one hopes to infer the distribution of incident gamma rays from the observed distribution of scatter cones. This part of the analysis can be called the “Compton telescope problem.” Indeed, astrophysicists working on the COMTEL satellite data (IEEE Trans on Nuclear Science NS31, 766-770 (1984)) performed the first analysis of this problem and produced sky maps of gamma-ray sources on the celestial sphere. However, clinical applications in nuclear medicine require the second part of the reconstruction problem; namely, the Compton camera must be moved around the patient and the parallax information used to produce a 3D mapping of the gamma-ray emissions within the body. This second part of the problem is generally ignored because (it is argued) the standard filtered back-projection techniques of reconstruction algorithms described in the last paragraph are actually solutions of the Compton telescope problem.
Compton cameras were first proposed in the 1970s, but have never fulfilled their promise of imaging with gamma-rays because the image reconstruction techniques were inadequate. A method is therefore desirable to improve gamma-ray image reconstruction techniques for use with Compton cameras. The present invention provides such a method.